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#### Tree reconstruction from multi-state characters

(University of Canterbury. Mathematics and Statistics., 2002)

In evolutionary biology, a character is a function from a set X of present-day species into a finite set of states. Suppose the species in X have evolved according to a bifurcating tree T. Biologists would like to use ...

#### A characterization for a set of partial partitions to define an X-tree

(University of Canterbury. Mathematics and Statistics., 2002)

Trees whose vertices are partially labelled by elements of a finite
set X provide a natural way to represent partitions of subsets of X. The condition under which a given collection of such partial partitions of X can be ...

#### Steady state optimal insulin infusion for hyperglycemic ICU patients

(University of Canterbury. Mathematics and Statistics.University of Canterbury. Mechanical Engineering., 2002)

Close control of blood glucose levels significantly reduces vascular complications in diabetes, as well as having beneficial effect for cardiac and other critical care patients. Recent studies have shown that tight regulation ...

#### Inverting random functions (II): explicit bounds for discrete maximum likelihood estimation, with applications

(University of Canterbury. Mathematics and Statistics, 2002)

In this paper we study inverting randomfunctions under the maximumlik elihood
estimation (MLE) criterion in the discrete setting. In particular, we consider how many independent
evaluations of the random function at a ...

#### Infinite anitchains of matroids with characteristics set {p}

(University of Canterbury. Mathematics and Statistics., 2002)

For each prime p, we construct an infinite antichain of matroids in which each matroid has characteristic set fpg. For p = 2, each of the matroids in our antichain is an excluded minor for the class of matroids representable ...

#### Active insulin infusion using optimal and derivative weighted control

(University of Canterbury. Mathematics and Statistics.University of Canterbury. Mechanical Engineering., 2002)

Close control of blood glucose levels significantly reduces vascular complications in Type I diabetes. A control method for the automation of insulin infusion that utilizes emerging technologies in blood glucose biosensors ...

#### On matroids of branch-width three

(University of Canterbury. Mathematics and Statistics., 2002)

For all positive integers k, the class Bk of matroids of branch-width
at most k is minor-closed. When k is 1 or 2, the class Bk is, respectively, the
class of direct sums of loops and coloops, and the class of direct ...

#### Projective Curvature and Integral Invariants

(University of Canterbury. Mechanical Engineering, 2002)

In this paper, an extension of all Lie group actions on R2 to coordinates
defined by potentials is given. This provides a new solution to the equivalence problems
of curves under the projective group and two of its ...